Problem: $\dfrac{ -6n - 5p }{ -2 } = \dfrac{ -2n + 5q }{ 4 }$ Solve for $n$.
Multiply both sides by the left denominator. $\dfrac{ -6n - 5p }{ -{2} } = \dfrac{ -2n + 5q }{ 4 }$ $-{2} \cdot \dfrac{ -6n - 5p }{ -{2} } = -{2} \cdot \dfrac{ -2n + 5q }{ 4 }$ $-6n - 5p = -{2} \cdot \dfrac { -2n + 5q }{ 4 }$ Multiply both sides by the right denominator. $-6n - 5p = -2 \cdot \dfrac{ -2n + 5q }{ {4} }$ ${4} \cdot \left( -6n - 5p \right) = {4} \cdot -2 \cdot \dfrac{ -2n + 5q }{ {4} }$ ${4} \cdot \left( -6n - 5p \right) = -2 \cdot \left( -2n + 5q \right)$ Distribute both sides ${4} \cdot \left( -6n - 5p \right) = -{2} \cdot \left( -2n + 5q \right)$ $-{24}n - {20}p = {4}n - {10}q$ Combine $n$ terms on the left. $-{24n} - 20p = {4n} - 10q$ $-{28n} - 20p = -10q$ Move the $p$ term to the right. $-28n - {20p} = -10q$ $-28n = -10q + {20p}$ Isolate $n$ by dividing both sides by its coefficient. $-{28}n = -10q + 20p$ $n = \dfrac{ -10q + 20p }{ -{28} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $n = \dfrac{ {5}q - {10}p }{ {14} }$